Find the locus of the centre of the circles of radius r which touch a given line l.

Dear Student,


$$\begin{gathered} Given : Circles with centres O , O\text{'} , O\text{'}\text{'} touching line T at P. \\ To Prove: To find the locus of centres of circles which touch \\ a given line at a given point. \\ Proof: As OP , O\text{'}P ,O\text{'}\text{'}P are the radii of the circles touching line T at P, \\ it is perpendicular to the given line. \\ As, OP , O\text{'}P , O\text{'}\text{'}P represent the same straight line pas\sin g through P and \perp \\ to PT. \\ Hence the locus of the centres of the circles which touch a given line at a \\ given point is a straight line to the given line at the given point. \end{gathered}$$


Hope this information will clear your doubts about topic.

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

Regards